But I want a dialog where the user can enter text (for example: if you download something with your browser you can type in the name of the file you want to save). I want to have such a window, but cannot find it.

You can make an activity that has the layout you want, then add the dialog style like this:

android:theme="@android:style/Theme.Dialog"

in the manifest. You can do pretty much anything you like in this activity. Use an intent to start it (you can send extras to preload it). Use startActivityForResult(Intent, requestcode) and receive the result back by overriding onActivityResult().

The example dialog is just an Activity, like any other. If you want it to have an EditText just put an EditText in the xml, instantiate it in the Java code and use it just like you would in any other activity. Take the result string and send it back in the extras. You can add the buttons and an icon, just like your picture. What makes it a dialog is the style in the manifest, starting it for a result and returning the result. That's what I was trying to show you how to do.